Premonoidal and Freyd categories are both generalized by non-cartesian Freyd categories: Effectful categories. We construct string diagrams for effectful categories in terms of the string diagrams for a monoidal category with a freely added object. We show that effectful categories are pseudomonoids in a monoidal bicategory of promonads with a suitable tensor product.
翻译:彩虹类和Freed类均按非cartesian Freyd 类别(效果类)普遍分类:效果类。我们为带有自由添加对象的一分子类的字符串图构建了效果类的字符串图。我们显示,效果类是具有适当粒子产品的一分子双类双胞胎类中的伪蛋白。